{"paper":{"title":"Exact asymptotics of the optimal Lp-error of asymmetric linear spline approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Dmytro Skorokhodov, Nataliya Parfinovych, Vladyslav Babenko, Yuliya Babenko","submitted_at":"2013-11-28T19:46:49Z","abstract_excerpt":"In this paper we study the best asymmetric (sometimes also called penalized or sign-sensitive) approximation in the metrics of the space $L_p$, $1\\leqslant p\\leqslant\\infty$, of functions $f\\in C^2\\left([0,1]^2\\right)$ with nonnegative Hessian by piecewise linear splines $s\\in S(\\triangle_N)$, generated by given triangulations $\\triangle_N$ with $N$ elements. We find the exact asymptotic behavior of optimal (over triangulations $\\triangle_N$ and splines $s\\in S(\\triangle_N)$ error of such approximation as $N\\to \\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7408","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}